What is the equation of the line shown in this graph?
The equation of a line is an algebraic form of representing the set of points, which together make up a line in a coordinate system. We have different forms of an equation of a line.
Answer: The equation of the line shown in this graph is y = (-1/2)x - 3
Let's analyze the given graph to find the equation of the line.
We know that the general equation of a straight line is given by y = mx + c
m = Slope of the line
c = y-intercept of the line
Given two points on a straight line (x1, y1) and (x2, y2) the slope is calculated by using the slope formula m = (y2 - y1) / (x2 - x1) ------ (1)
Let's look into the graph shown below
From the graph we see that, the coordinates (x1, y1) and (x2, y2) are A (-6,0) and B (0,-3), respectively.
Let's calculate the slope 'm' using equation (1).
m = (-3 - 0) / (0 - (-6))
m = -3 / 6 = -1 / 2
You can use Cuemath's online slope calculator to find the slope.
Also, we see that the line cuts the y-axis at y = -3
Thus, the y-intercept is c = -3
Substituting the values of 'm' and 'c' in y = mx + c we get,
y = (-1/2)x - 3